Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann model is proposed. It is showed that the accelerated expanding universe is guaranteed by a constrained RandersFinsler structure without invoking dark energy. The geodesic in Randers-Finsler space is studied. The additional term in the geodesic equation acts as repulsive force against the gravity. PACS numbers: 02.40.-k, 04.50.Kd, 95.36.+x, 98.80.Jk [email protected] [email protected] 1 Einstein’s general relativity connects the Riemann geometry to gravitation. It is the standard model of gravity. However, up to now, general relativity still faces problems. One of them is that the flat rotation curves of spiral galaxies violate the prediction of Einstein’s gravity. Another is related with recent astronomical observations[1]. Our universe is acceleratedly expanding. This result can not be obtained directly from Einstein’s gravity and his cosmological principle. The most widely adopted way to resolve these difficulties is the dark matter and dark energy hypothesis. However, up to now, such things can not be detected directly from observations. This situation causes that some physicists imagine the dark matter and dark energy hypothesis possesses some properties of the ether hypothesis at the early 20 century. It is reasonable to test the connection between gravitation and new geometry. Modified Einstein’s gravity may throw new light to the above problems. Models have been built for alternative to the dark matter hypothesis. The famous one is the modified Newtonian dynamics[2]. Models have also been built for alternative to the dark energy hypothesis[3]. Finsler geometry, which takes Riemann geometry as its special case, is a good candidate to solve the problems mentioned above. In our previous paper[4], a modified Newton’s gravity was obtained as the weak field approximation of the Einstein’s equation in Finsler space of Berwald type. We have shown that the prediction of the modified Newton’s gravity is in good agreement with the rotation curves of spiral galaxies without invoking of dark matter hypothesis. In this Letter, we propose a modified